Archimedes discovered that the area of the region bounded by a parabola and a chord is 2/3 the area of its circumscribing parallelogram with two sides parallel to the parabola's axis. We show that parabolic arcs are the only smooth strictly convex functions with the 2/3-property, where two sides of the circumscribing parallelogram are parallel to the y-axis.
展开▼